dcbb5           package:mlCopulaSelection           R Documentation

_B_B_5 _c_o_p_u_l_a _d_e_n_s_i_t_y _f_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Calculate the value of the BB5 density.

_U_s_a_g_e:

     dcbb5(theta, delta, u, v)

_A_r_g_u_m_e_n_t_s:

   theta: Parameter 'theta' of the BB5, (1<'theta').  

   delta: Parameter 'delta' of the BB5, (0<'delta'). 

       u: First coordenate where de density will be evaluated.
          (0<'u'<1)

       v: Second coordenate where de density will be evaluated.
          (0<'v'<1)

_V_a_l_u_e:

     value of de density BB5 for the parameters  'theta'  and  'delta'
     on ( 'u' ,  'v' )

_A_u_t_h_o_r(_s):

     Jesus Garcia, IMECC-UNICAMP and  Veronica Gonzalez-Lopez,
     IMECC-UNICAMP

_R_e_f_e_r_e_n_c_e_s:

     Joe, H., (1997). Multivariate Models and Dependence Concepts. 
     Monogra. Stat. Appl. Probab. 73, London: Chapman and Hall.

_E_x_a_m_p_l_e_s:

     res<-dcbb5(1.5,1.5,0.75,0.6)

     ## The function is currently defined as
     function(theta,delta,u,v)
     {t<-(-log(u))^(-theta*delta)+(-log(v))^(-theta*delta);
             dut<-(theta*delta/u)*(-log(u))^(-theta*delta-1);
             dvt<-(theta*delta/v)*(-log(v))^(-theta*delta-1);
             S<-(-log(u))^(theta)+(-log(v))^(theta);
             duS<-(-theta/u)*(-log(u))^(theta-1);
             dvS<-(-theta/v)*(-log(v))^(theta-1);
             h<-S-t^(-1/delta);
             duh<-duS+(1/delta)*(t)^(-1/delta-1)*(dut);
             dvh<-dvS+(1/delta)*(t)^(-1/delta-1)*(dvt);
             dvuh<--1/delta*(1/delta+1)*t^(-1/delta-2)*dut*dvt;
             densi<-exp(-h^(1/theta))*(1/theta)^2*(h^(1/theta-1))^2*dvh*duh+exp(-h^(1/theta))*(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh+exp(-h^(1/theta))*(-1/theta)*h^(1/theta-1)*dvuh
             }

